A man who makes, sells, or wears bonnets; a male milliner or bonnet merchant.
Compound of 'bonnet' plus 'man', following the standard English pattern of adding 'man' to indicate a male professional associated with a particular trade or object.
While 'milliner' was the usual term, 'bonnetman' specifically emphasizes making or dealing in bonnets—and it's mostly a historical term, as the bonnet trade declined in the 20th century!
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